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摘要: 相机全局位置估计作为运动恢复结构算法（Structure from motion，SfM）中的核心内容一直以来都是计算机视觉领域的研究热点.现有相机全局位置估计方法大多对外点敏感，在处理大规模、无序图像集时表现的尤为明显.增量式SfM中的迭代优化步骤可以剔除大部分的误匹配从而降低外点对估计结果的影响，而全局式SfM中没有有效地剔除误匹配的策略，估计结果受外点影响较大.针对这种情况，本文提出一种改进的相机全局位置估计方法：首先，结合极线约束提出一种新的对误匹配鲁棒的相对平移方向估计算法，减少相对平移方向估计结果中存在的外点；然后，引入平行刚体理论提出一种新的预处理方法将相机全局位置估计转化为一个适定性问题；最后，在此基础上构造了一个对外点鲁棒的凸优化线性估计模型，对模型解算获取相机位置估计全局最优解.本文方法可以很好地融合到当下的全局式SfM流程中.与现有典型方法的对照实验结果表明：在处理大规模、无序图像时，本文方法能显著提高相机全局位置估计的鲁棒性，并保证估计过程的高效性和估计结果的普遍精度.Abstract: As a core module of structure from motion (SfM), location estimation of cameras in a global framework has been a research hotspot of computer version. State-of-the-art methods for location estimation are sensitive to outliers, especially for large scale, unordered images. The incremental SfM reduces the influence of outliers through an iterative optimization. The global SfM does not have an efficient strategy to remove mismatch, so the result of estimation is influenced deeply by outliers. Therefore, we introduce an improved method for location estimation. First, combined with the epipolar constraint we propose a new pairwise direction estimation algorithm. Then, we make the problem well-posed by introducing a new preprocessing method based on parallel rigidity. Finally, we propose a robust linear estimation model based on convex programing. We can get a global optimum solution by resolving this model. The method can integrate well with state-of-art global SfM pipeline. Multiple group experiments have proved the robustness of our methods without any loss of efficiency and common precision.1) 本文责任编委 贾云得
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图 1 融合本文改进的全局式SfM算法流程图
Fig. 1 The processing pipeline of global SfM fusion our modifying
图 2 本文改进的相对平移方向估计算法流程
Fig. 2 The processing pipeline of relative translation estimation based on our modifying
图 11 利用本文算法对8组公开数据集处理获取的场景三维稀疏结构
Fig. 11 The experimental result with 8 groups of datasets based on our method
图 6 相机全局位置散点图(数据Vienna, 相机个数821)
Fig. 6 Global location of cameras represented by scatter diagram
图 7 BA优化后本文同1DSfM实验结果平均值比较图
Fig. 7 Comparison result of mean between our method and 1DSfM after BA
图 9 BA优化前本文同1DSfM实验结果中位数比较图
Fig. 9 Comparison result of median between our method and 1DSfM before BA
图 10 BA优化后本文同1DSfM实验结果中位数比较图
Fig. 10 Comparison result of median between our method and 1DSfM after BA
数据 本文方法 1DSfM [23] [20] 初始 BA后 初始 BA后 BA后 名称 尺寸(像素) 数目 $\widetilde{x}$ $\overline{x}$ $N$ $\widetilde{x}$ $\overline{x}$ $\widetilde{x}$ $N$ $\widetilde{x}$ $\overline{x}$ $N$ $\widetilde{x}$ Tower 1 600×1 064 1 576 3.4 19 461 1.3 22 11 414 1.0 40 306 44 Montreal 1 349×1 600 2 298 0.6 1 454 0.4 1 2.5 427 0.4 1 357 9.8 Madrid 1 600×1 081 1 344 2.3 5 337 1.0 4 9.9 291 0.5 70 240 18 Piazza 1 600×2 390 2 251 1.8 5 318 1.0 3 3.1 308 2.1 200 93 16 Yorkminster 1 600×2 129 3 368 2.7 6 406 1.4 4 3.4 401 0.1 500 345 6.7 Library 1 067×1 600 2 550 2.3 6 321 0.7 5 2.5 295 0.4 1 271 1.4 Vienna 1 600×2 400 6 288 6.5 16 821 2.2 10 6.6 770 0.4 2E4 652 12 Alamo 1 600×2 133 2 915 0.5 2 554 0.4 2 1.1 529 0.3 2E7 422 2.4 
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表 2 本文方法同1DSfM、文献[20]、Bundler处理时间比较
Table 2 Comparison of efficiency: our method、1DSfM、Bundler and [20]
数据 本文方法 1DSfM [23] [20] Bundler $T_R$ $T_O$ $T_S$ $T_{BA}$ $\Sigma$ $T_R$ $T_O$ $T_S$ $T_{BA}$ $\Sigma$ $\Sigma$ $\Sigma$ Tower 1 29 9 351 390 9 14 55 606 648 264 1 900 Montreal 2 66 24 352 444 17 22 75 1 135 1 249 424 2 710 Madrid 1 12 7 158 178 15 8 20 201 244 139 1 315 Piazza 1 14 11 95 121 14 9 35 191 249 138 1 287 Yorkminster 1 31 12 128 172 11 18 93 777 899 394 3 225 Library 1 13 6 199 219 9 13 54 392 468 220 3 807 Vienna 6 344 50 1 206 1 606 98 60 144 2 837 3 139 2 273 10 276 Alamo 4 153 49 847 1 053 56 29 73 752 910 1 403 1 654
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